Dan (or Steve, or both) is the subject of this sentence, not the object.
You may be right about that (I’m not sure) but it doesn’t effect the argument.
In both sentences, the pronoun used has two possible meanings in that context.
What are the two meanings (senses) of the word “he” in your sentence? It only seems to have one meaning from what I can tell.
As I understand it, in both sentences there are two subjects (using your terminology) but in my sentence, the pronoun has more than one sense whereas in your sentence the pronoun has only one sense. The multiple senses of the pronoun in my sentence is the cause of the problem, not the multiple subjects.
In my sentence it’s also possible that there is the same ambiguity of subjects as in yours but that is not a given because it depends on which of the senses of the pronoun is intended. And that isn’t clear. Which is the problem.
What are the two meanings (senses) of the word “he” in your sentence?
Dan or Steve is what I mean here — meanings within the context of their usage, not in an isolated sense. These meanings would both be described as “third person singular male pronoun” in a dictionary, but by the nature of a pronoun the whole point is for it to refer to something you’ve already talked about in context
The multiple senses of the pronoun in my sentence is the cause of the problem, not the multiple subjects.
We can test for this. If there’s only one subject, Dan, then the sentence becomes:
“I was with Dan (they/them) the other day. They hadn’t brought a poster they needed and went back to the car to get it.”
No ambiguity there, it can only mean Dan. Similarly, with a single subject that consists of multiple people:
“I was with the newlyweds the other day. They hadn’t brought a poster they needed and went back to the car to get it.”
Exact same thing, no ambiguity. So we can use “they” in both senses and it’s totally fine so long as there’s only one subject. The ambiguity comes about when there are two possibilities already mentioned that the pronoun could potentially refer to — just like if Dan and Steve are both “he”.
Again, we’re talking about different linguistic issues, which I’ll demonstrate below. I see now that my example wasn’t a good example because it conflates a consequence of the problem with the problem itself.
The ambiguity
There are two different ambiguities. You’re talking about ambiguity over the subject whereas I’m talking about ambiguity over the sense of the pronoun.
“I was with Dan (they/them) the other day. They hadn’t brought a poster they needed and went back to the car to get it.”
No ambiguity over sense of “they”. No ambiguity over subject.
“I was with the newlyweds the other day. They hadn’t brought a poster they needed and went back to the car to get it.”
No ambiguity over sense of “they”. No ambiguity over subject.
“I was with Dan (he/him) and Steve (he/him) the other day. He hadn’t brought a poster he needed and went back to the car to get it.”
No ambiguity over sense of “he”. Ambiguity over subject.
“I was with Dan (they/them) and Steve the other day. They hadn’t brought a poster they needed and went back to the car to get it.”
Ambiguity over sense of “they”. Ambiguity over subject.
The ambiguity over the sense of the pronoun is the confusion. That’s the problem. The ambiguity over the subject is a problem but not the problem I meant.